Question 13.10: Ages of Substance Abuse Program Participants Twenty people e......

Step 1 State the hypotheses and identify the claim.

H_{0} : The ages of the people, according to the order in which they enroll in a substance abuse program, occur at random (claim).

H_{1} : The ages of the people, according to the order in which they enroll in a substance abuse program, do not occur at random.

Step 2 Find the critical value.

Find the median of the data. Arrange the data in ascending order.

18 19 19 19 20 22 22 23 25 27 27

28 32 35 36 37 43 43 44 46

The median is 27 .

Replace each number in the original sequence as written in the example with an \mathrm{A} if it is above the median and with a \mathrm{B} if it is below the median. Eliminate any numbers that are equal to the median.

Recall the original sequence is 18,36,19,22, \ldots, 22. Then

18 is below the median, so it is \mathrm{B};

36 is above the median, so it is \mathrm{A};

19 is below the median, so it is \mathrm{B};

etc.

The sequence of letters, then, is

B A B B B A B A B A A A A A A B B B

There are 9 A’s and 9 B’s. Table M shows that with n_{1}=9, n_{2}=9, and \alpha=0.05, the number of runs should be between 5 and 15 .

Step 3 Find the test value. Determine the number of runs from the sequence of letters.

\begin{array}{|c|l|} \hline \text{Run }& \text{Letters }\\ \hline 1 & B \\ 2 & A \\ 3 & B B B \\ 4 & A \\ 5 & B \\ 6 & A \\ 7 & B \\ 8 & AAAAAAA \\ 9 & B B B \\ \hline \end{array}

The number of runs G=9.

Step 4 Make the decision. Since there are 9 runs and 9 falls between the critical values 5 and 15 , the null hypothesis is not rejected.

Step 5 Summarize the results. There is not enough evidence to reject the hypothesis that the ages of the people who enroll occur at random.